Abstract
We present a simple, new method for the 1-loop renormalization of integrable σ-models. By treating equations of motion and Bianchi identities on an equal footing, we derive ‘universal’ formulae for the 1-loop on-shell divergences, generalizing case-by-case computations in the literature. Given a choice of poles for the classical Lax connection, the divergences take a theory-independent form in terms of the Lax currents (the residues of the poles), assuming a ‘completeness’ condition on the zero-curvature equations. We compute these divergences for a large class of theories with simple poles in the Lax connection. We also show that ℤT coset models of ‘pure-spinor’ type and their recently constructed η- and λ-deformations are 1-loop renormalizable, and 1-loop scale-invariant when the Killing form vanishes.
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Levine, N. Universal 1-loop divergences for integrable sigma models. J. High Energ. Phys. 2023, 3 (2023). https://doi.org/10.1007/JHEP03(2023)003
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DOI: https://doi.org/10.1007/JHEP03(2023)003